Einstein–Cartan–Dirac theory in (1+2)-dimensions

Abstract

Einstein–Cartan theory is formulated in (1+2) dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space–time torsion is found to be given algebraically in terms of a quadratic spinor condensate field. Circularly symmetric, exact solutions that collapse to AdS 3 geometry in the absence of the Dirac condensate are found.